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Solid State Sciences 11 (2009) 760–765

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Solid State Sciences

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Magnetic anisotropy and molecular assembling in d complex cation–f complexanion type coordination compounds

Marilena Ferbinteanu a,*, Fanica Cimpoesu b, Takashi Kajiwara c,d, Masahiro Yamashita c,d

a University of Bucharest, Faculty of Chemistry, Inorganic Chemistry Laboratory, Dumbrava Rosie 23, Bucharest 020462, Romaniab Institute of Physical Chemistry, Splaiul Independentei 202, Bucharest 060021, Romaniac Tohoku University, Graduate School of Science, Department of Chemistry, Aramaki, Aoba-ku, Sendai 980-8578, Japand CREST, Japan Science and Technology Agency (JST), Japan

a r t i c l e i n f o

Article history:Received 6 June 2007Received in revised form 6 June 2008Accepted 9 June 2008Available online 17 June 2008

Keywords:d and f complexesLanthanide complexesMagnetic anisotropyAb initio calculationsChemical bondingDonor–acceptor perturbationSupramolecular assembling

* Corresponding author. Tel.: þ40 21 2103497; fax:E-mail address: marilena.cimpoesu@g.unibuc.ro (M

1293-2558/$ – see front matter � 2008 Elsevier Masdoi:10.1016/j.solidstatesciences.2008.06.008

a b s t r a c t

The system [Fe(bpca)2][Er(NO3)4(H2O)2] (1) (Hbpca¼ bis(2-pyridil-carbonyl) amine) is a complex cation–complex anion type coordination compound consisting of distinct d and f units, interlinked by hydrogenbonds. Particularly, the association of f-type complex anions in dimers is remarked and discussed. Theenergy decomposition analyses based on DFT calculations offered supplementary insight into thecoordination effects at the lanthanide ions and the hydrogen bond driven supramolecular association ofthe complex units. Special ab initio procedures and subsequent modeling afforded the computation ofanisotropic magnetization tensors of the [Er(NO3)4(H2O)2]� f-type units. The computed results are in linewith the experimental data for compound 1.

� 2008 Elsevier Masson SAS. All rights reserved.

1. Introduction

The Single Molecule Magnet (SMM) [1] and Single Chain Magnet(SCM) [2] paradigms had initiated large impetus in various areas ofcoordination magneto-chemistry, synthetic, instrumental andtheoretical, bringing into focus the issues of magnetic anisotropy,which make lanthanide chemistry a challenging chapter ofmolecular magnetism. The lanthanide complexes show a largestructural variety [3] including peculiarities such as the occurrenceof SMM effects at low nuclearities, e.g. d–f binuclears [4] or evenlanthanide mononuclears [5]. The challenging magnetic andstructural problems of d–f systems attracted our interest [4a,6],presenting here a new case study. The magnetic anisotropy of the funits and the assembling factors are discussed in experimental andtheoretical respects.

The complex cation–complex anion type coordinationcompound [Fe(bpca)2][Er(NO3)4(H2O)2] (1) (Hbpca¼ bis(2-pyridil-carbonyl) amine) has distinct d and f units, weakly connected byhydrogen bonds. The d sphere, [Fe(bpca)2]þ, is the cationic unit,made with tridentate bpca� ligands. The anionic counterpart is thelanthanide complex [Er(NO3)4(H2O)2]�, having the nitrate ligands

þ40 21 3159249.. Ferbinteanu).

son SAS. All rights reserved.

in quasi-equatorial placement and trans-position of the aqualigands. The experimental data were complemented with ab initioinsight into the coordination bonding, supramolecular assemblingand magnetic anisotropy.

2. Experimental and calculation details

2.1. Preparation

All chemicals and solvents were used as received and nopurification was needed. Compound 1 was obtained by addinga solution of Er(NO3)3$6H2O (0.05 mmol) in methanol/nitrometh-ane (0.25 mL/1.75 mL) to an equimolar solution of [Fe(bpca)2]NO3

(synthesized as described elsewhere [7]) in nitromethane (2 mL).After 30 min stirring at room temperature, the solution was leftundisturbed. Well-formed orange crystals were obtained afterseveral days (yield 67%). Crystals were used for X-ray analysis andmagnetic measurements. Anal. Calcd for 1, C24H16ErFeN10O18: C,30.17; N, 14.66; H, 1.69. Found: C, 30.41; N, 14.78; H, 1.53.

2.2. Single crystal X-ray analysis

The data were collected on a SMART-1000/CCDD (Bruker AXS)area detector using the standard procedure (Mo Ka radiation). The

M. Ferbinteanu et al. / Solid State Sciences 11 (2009) 760–765 761

data integration and reduction were undertaken with SAINT andXPREP [8]. The intensity data were empirically corrected forabsorption by using the program SADABS [9]. The structures weresolved by direct methods using SHELXS-97 and refined usingleast-squares methods on F2 with SHELXL-97 [10]. Non-hydrogenatoms were modeled with anisotropic displacement parameters,and hydrogen atoms were placed by difference Fourier synthesesand refined isotropically. Ka¼ 0.71073 Å, T¼ 100 K, orange blocks,formula C24H16ErFeN10O18, MW¼ 955.58, 0.40� 0.14� 0.10 mm,triclinic, P-1, a¼ 10.2029(9) Å, b¼ 10.6203(9) Å, c¼ 15.2040(13) Å,a¼ 86.857(3)�, b¼ 73.651(2)�, g¼ 86.618(2)�, Z¼ 2, V¼ 1576.8(2) Å3,R1¼0.0253, wR2¼ 0.0580, GooF¼ 1.046. See Table 1 for selectedbond lengths and angles. Fig. 1 gives an ORTEP representation withthe atom numbering scheme.

2.3. Magnetic measurements

Magnetic measurements were carried out on a Quantum DesignSQUID MPMS 5S magnetometer on polycrystalline samples. DCmeasurements were made using an external magnetic field of1000 Oe over a temperature range of 1.8–300 K and AC measure-ments using a 3-Oe magnetic field oscillating at 10–1400 Hz.Diamagnetic corrections were estimated from Pascal’s constant.

2.4. Ab initio calculations

The CASSCF (Complete Active Space Self-Consistent Field) andspin orbit calculations were performed with the GAMESS program[11], using SBKJC effective core potential and basis set for Er(III) and6-311G* basis set for the ligands. The bonding in the model Lu(III)complexes was analyzed by DFT calculations (Density FunctionalTheory) with ADF (Amsterdam Density Functional) code [12], usinggradient corrected Becke–Perdew functional and the TZP basis set.We relaxed the frozen core AOs of the lanthanide, erasing thecorresponding constraint from small-core TZP default file, consid-ering then self-consistently the all-electrons system. The NaturalBond Orbital (NBO) method [13], subsequent to the DFTcalculations, used the NBO 5 code [14].

3. Results and discussion

3.1. Structure description

The complex cation, [Fe(bpca)2]þ, and complex anion,[Er(NO3)4(H2O)2]�, of compound 1 are, in a first approximation,separated units (see Figs. 1 and 2), while in closer detail there isa hydrogen bond network linking cations to anions and the anionsin f–f dimeric associations. The lattice does not contain solventmolecules, so that the entire hydrogen bonding is established bythe aqua ligands coordinated at the Er(III). The d–f unit linkage ismade by HOH/O]Co bridges established with the emergentcarbonyl groups of the bpca� ligand. The f–f dimerization is done bythe HOH/ONO2

� sequence between the aqua ligand of onelanthanide unit and the nitrate ligand of another one (O12/H17distance 2.159 Å). The bi-negative f–f dimer shows center of

Table 1Bond lengths (Å) and selected angles (�)in the [Fe(bpca)2]þ cationic d unit

Bond length (Å) Bond angles (Degrees)

Fe1–N1 1.981(3) N1–Fe1–N3 163.65(12)Fe1–N3 1.984(3) N2–Fe1–N1 81.75(12)Fe1–N2 1.922(3) N2–Fe1–N3 81.95(12)Fe1–N4 1.958(4) N4–Fe1–N6 165.67(13)Fe1–N6 1.970(3) N5–Fe1–N4 83.09(14)Fe1–N5 1.889(3) N5–Fe1–N6 82.76(14)

inversion. The hydrogen bonds between the d and f units areestablished with the following contacts: O1/H19¼1.718 Å, O2B/H20¼ 2.143 Å and O3/H18¼ 1.859 Å.

The [Fe(bpca)2]þ is a distorted octahedron, the stereochemistry ofwhich is imposed by the strains due to specific geometry oftridentate bpca� ligands. It shows compression along one axis (seethe Fe1–N2 and Fe1–N5 bonds in Table 1) and out-of-plane slightpuckering of the atoms comprising the equatorial zone, so that thebond angles differ with certain extent from the ortho-axial frame (seebond angles in Table 1). The [Er(NO3)4(H2O)2]� is a 10-coordinatedunit, with four nitrate chelates in the equatorial zone. The twomonodentate aqua ligands are placed in trans, with the open angleO17–Er1–O18¼ 150.65(11)�, sketching an approximate axis,perpendicular to the average plane of N atoms from the four nitrateligands. For sake of better systematization, in the view of ulterior abinitio analysis, we labeled the six ligands in the f coordination unit asshown in Fig. 1. The geometry data in Table 2 are organized withrespect to this supplementary labeling. One notes that the nitratechelation is, for each ligand, asymmetrical with one Er/O bondslightly elongated.

3.2. Magnetic properties

The cT product (Fig. 3) at room temperature is about 12 cm3 K/mol, which roughly corresponds to a sum of effective 4I15/2 groundstate (treatable by gJ¼ 1.2, J¼ 15/2 ideal values) on Er(III) with theFe(III) paramagnet (gS¼ 2, S¼ 1/2). The ascendant cT vs. Tresembles the antiferromagnetic pattern, but it cannot be assignedin such a simplistic way. Most probably, the Er(III) single ionanisotropy is the origin of the cT function. The growth from8.5 cm3 K/mol at 1.8 K to 12 cm3 K/mol at 300 K is progressive on allthese temperature domains. This suggests a statistics over energygaps larger than those conceivable for d–f or f–f exchange couplings[4a,6]. The maximum recorded magnetization reaches about 7.5 mB

at 50 kOe at 1.8 K, the slope showing still increasing trend, toa plateau gJ,$J w 9 mB reachable, in principle, for the above-mentioned ideal parameters.

3.3. Ab initio computed magnetic anisotropy

The calculation of lanthanide complexes implies specialprocedures [4a,6]. Because of non-Aufbau electron configuration,the multi-configuration calculations cannot be started properlyfrom a single determinant available reference. In turn, wesucceeded in obtaining reliable converged solution by starting witha wavefunction assembled from preliminary computed Er(III) andligand fragments.

The CASSCF(11,7) calculation (i.e. 11 electrons in 7 selectedorbitals) corresponding to the f11 configuration of the Er(III) in the[Er(NO3)4(H2O)2]� complex was done under state average on 13levels related to the Ligand Field (LF) split of the 4I multiplet. TheSpin Orbit (SO) calculations yielded 52 states, corresponding to thesplit LFþ SO spectrum from all 4IJ states with J between 9/2 and 15/2. The lowest states from CASSCFþ SO computation (accounting forthe LFþ SO effects) are a series of 8 doubly degenerate pairs, whosefull gap falls in the 300 cm�1 range. These pairs follow only formallythe �Jz labels (from �1/2 to �15/2) while, rigorously speaking, theJz cannot be numerically assigned and taken as a quantum number.This LFþ SO interplay is qualitatively similar to the ZFS effect, butthe term spacing does not obey the usual ZFS Hamiltonians.

The CASSCFþ SO calculations afforded the information neededto build the orbital part of the Zeeman Hamiltonian. Using thecorresponding data, we modeled the further splitting of LFþ SOstates in magnetic field, with a separate original computer code.The magnetization tensors of the lowest state were obtained fromthe response of energy as a function of various orientations of

Fig. 1. The asymmetric unit of compound 1. The labels in the curled brackets serve to the identification of the ligands in the f complex in the subsequent discussion.

M. Ferbinteanu et al. / Solid State Sciences 11 (2009) 760–765762

magnetic field. The energy derivative with respect to magnetic fieldon all space orientations is represented as a polar diagram (Fig. 4),yielding the magnetization tensor in the given molecular frame.

The maximal extension along the easy magnetization axis is atabout 5 mB. If the Jz were a good quantum number, the magneti-zation tensor of various states would have the gJJz mB maximalextension between 0.6 mB and 9 mB. The actual 5 mB maximal valueon the ground state easy magnetization axis suggests a momentumadmixed and irregular ordering with respect to the Jz expectationvalues. This seems in line with the experimental cT dependence. AtT / 0 limit, assuming the cT dominated by an effective Jz

eff

assignable to the lowest state, the recorded 8.5 cm3 K/mol mini-mum, equated by (NAmB

2/kB)(gJJzeff)2 fits a gJ$Jz

eff amount of 4.7 mB,reasonably close to the extension estimated from ab initio

Fig. 2. Packing diagram of compound 1, emphasizing by space filled representation the hydras wireframe. Note that the lattice does not contain solvent molecules.

anisotropy. One may also assume the high temperature limit due toa J momentum paramagnet, close to the ideal value (NAmB

2/3kB)gJ

2J(Jþ 1)¼ 12.825 cm3 K/mol. This will correspond to the casewhen thermal promotion overrides, by averaging, all the LFþ SOeffects and the resulted ZFS-like splitting. Thus the cT vs. T exper-imental dependence appears as an evolution between effectiveintermediate moment Jz

eff of the ground state from irregularZFS-like spectrum, towards the paramagnetic limit estimated withthe full J moment of the lanthanide center. The thermal averagingtends to be reached up to the room temperature, where the kTbecomes comparable with the ab initio total splitting of the lowestsequence of the LFþ SO scheme (300 cm�1). The ab initio calcula-tions served to foresee this interpretation, even though the resultedabsolute parameters should be considered semi-quantitatively.

ogen bonded dimeric units [Er(NO3)4(H2O)2]�2, while the [Fe(bpca)2]þ are represented

Table 2Bond lengths (Å) and selected angles in the [Er(NO3)4(H2O)2]� anionic f unit, orderedas a function of ligand labeling, correspondent to those in curly brackets in Figs. 1and 5

Ligandno.

Ligandtype

O label i O label j Er–Oi (Å) Er–Oj(Å) Oi–Er–Oj

1 NO3� 8 10 2.437(3) 2.420(2) 52.61(9)

2 NO3� 11 13 2.500(2) 2.468(3) 51.38(8)

3 NO3� 5 7 2.588(3) 2.377(3) 51.39(9)

4 NO3� 14 15 2.404(3) 2.462(3) 52.78(9)

5 H2O 17 2.314(3)6 H2O 18 2.368(3)

The crystallographic labels of the involved oxygen atoms are given in the i and jcolumns.

Fig. 4. The magnetization tensor for the ground state of the [Er(NO3)4(H2O)2]� units,obtained via CASSCFþ SO ab initio calculations followed by the modeling of magneticfield response properties.

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3.4. Coordination and supramolecular association energies

We consider in the following the ab initio insight into thecoordination and assembling of the discussed lanthanide dimers. Inorder to focus on such aspects using certain facilities of DFT codeslike the ADF [13], we will consider replacing Er(III) with Lu(III) inthe following computation experiments. Thus, by using the closedshell f14 of Lu(III) instead of open f11 configuration of Er(III), on thesubstantiated ground of the fact that the f shell does not contributeto the bonding, one may discriminate the other significantmolecular and supramolecular factors of the assembling.

The philosophy behind the ADF code is particularly convenient.Namely, the calculation is started from preliminarily preparedfragments, while the output reports and analyses the energy offormation with respect to such defined units, taken as zero of thescale. As a function of fragment preparation procedures, oneobtains different data. Thus, taking as fragments a given ligand andthe remainder of the complex, e.g. NO3

� vs. [Lu(NO3)3(H2O)2], orH2O vs. [Lu(NO3)4(H2O)]�, one obtains quantities that can beassigned to the coordination strength of the given ligand (lines 1–6in Table 3). If defined as fragments the Lu(III) ion and all theseparate ligands, the total energy of coordination is estimated (line7 in Table 3). Finally, working with two separate [Lu(NO3)4(H2O)2]�

units as pre-defined fragments forming the dimer, we investigatetheir supramolecular association energy (line 8 in Table 3).

In order to assess the scale reliability of the outlined results, it isinstructive to do a rough estimation, considering point charges, i.e.þ3 as Ln(III) and four �1 ones placed at the barycenter of eachnitrate ligand (at about 2.8 Å from center). The total energy of pointcharge association is�946 kcal/mol, with the net metal–ligand partof�1400 kcal/mol. Comparing these amounts with line 7 of Table 3

Fig. 3. Temperature dependence of cT for 1. Inset: the magnetization vs. field (1.8 K).

one sees that the range is in line both with the computed electro-static association, and also with the total bonding energy. This canbe taken as an expression of the fact that, besides different quan-tum effects, the bonding can be thought effectively of ionic type.Taking the same simplistic model, one estimates the associationenergy of one negative point charge ligand against the remainingcharge points at about �140 kcal/mol. This parallels also the rangecomputed for bonding and electrostatic energies of individualnitrate ligands, in the lines 1–4 of Table 3. After this check we canperceive correspondingly the computed quantities.

Thus, by certain compensation of different components, thetotal bonding energy is comparable to the net electrostatic attrac-tion from brute point charge estimation (for each charged ligandand for the whole coordination sphere too). However, there isa significant orbital stabilization established with the help of 5dand 6s AOs of the lanthanide (see orbital part column in Table 3).The closed shell repeal of metal ion and ligands is reflected in thePauli’s repulsion computed within ADF procedures. For chargedligands this amount is about 2/3 from absolute value of thecomputed Coulomb part. For the neutral ones the two quantitiesalmost compensate each other, so that, one may assign the effectivebinding to orbital effects.

Complementary information is added by the donor–acceptoranalysis performed by the Natural Bond Orbital (NBO) method [14]subsequent to the outlined DFT calculations. We must note that thedonor–acceptor quantities are not directly corresponding toa bonding energy, being just a component of it, in alternativeanalysis. However, both donor–acceptor parts, as well as the above-discussed dichotomized components, are paralleling the trend ofthe formation energies along the given series of ligands. The naturalbond orbitals that resulted were assigned to the separated units ofmetal and ligands. Summing the corresponding perturbationcomponents between occupied and virtual NBOs of different frag-ments one may present the ligand-to-metal donation effects aswell as metal-to-ligand back-donation amounts, as seen in the lastcolumns of Table 3. The values must be considered in a semi-quantitative sense, since the perturbation procedure implies some

Table 3The energy of bonding and dichotomized components

Separated fragments ADF energy analysis NBO donor–acceptor

Total bonding Orbital part Pauli repulsion Electro-static L–M M–L

1 NO3� (1) �151.4 �130.6 65.5 �86.4 �230.9 �218.6

2 NO3� (2) �134.9 �106.1 59.7 �88.5 �179.9 �180.6

3 NO3� (3) �140.5 �109.3 56.8 �88.0 �184.8 �187.9

4 NO3� (4) �155.5 �123.9 65.5 �97.1 �225.4 �242.1

5 H2O (5) �76.3 �78.1 42.9 �41.2 �107.1 �144.66 H2O (6) �69.4 �71.0 32.6 �31.0 �97.3 �192.77 4�NO3

� 2�H2O �1492.5 �585.3 293.3 �1200.58 Inter-molecular �3.0 �40.3 14.7 22.6

The energy of bonding and dichotomized components: with respect to binding of each ligand to a pre-formed fragment of corresponding complex remainder (lines 1–6); withrespect to total association of separate ligand and metal ion fragments (line 7); and the supramolecular assembling in dimer, with respect to pre-formed mononuclearcomplexes (line 8). All the quantities are in kcal/mol, from DFT calculations to ADF code.

M. Ferbinteanu et al. / Solid State Sciences 11 (2009) 760–765764

approximations in their obtaining. However, in relative compari-son, the results are meaningful and interesting.

Though apparently counterintuitive, the donation and back-donation effects are comparable. The back-donation (filled AOs ofmetal ion against diffuse virtual MOs of the ligand) consists in eachcase of about 87% contribution from s occupied shells of lanthanide,12% from d occupied shells, with practically negligible role of p AOsand definitely null contribution of the f shell. The prevalence of sshell comes from the density tails of large quantum numbers 5s and4s. The slight s–d mixing into the natural hybrid orbitals computedby NBO procedures suggests that the d is brought into interactionrather indirectly, via the interaction propensity of the s orbitalchannel. Conversely, there is no mixing of p shells with others,because the ligand environment cannot enforce significant polardeformation of the electronic cloud of the metal ion. Consequently,the p shell remains rather inactive in the back-donation effects.

The fact that the f shell shows absolute zero contribution to theback-donation effect is an important quantitative confirmation ofits intuitively acknowledged chemical inertness. This offers alsoulterior justification of the use of Lu(III) instead of Eu(III) in thenumerical experiments pursuing the evaluation of coordinationand supramolecular association energies. Here is the place to recallin certain detail the fact of non-Aufbau configuration of thelanthanide complexes. Thus, in the [Lu(NO3)4(H2O)2]� complex, theMOs having practically 100% f AO nature are placed between 60 and66 order numbers, showing very small ligand field splitting(�14.057 to �14.014 eV), while the HOMO level is at the MOnumber 108, with�3.044 eV. The situation remains in principle thesame for partly filled f complexes. This non-Aufbau configuration ofopen shell lanthanide complexes causes severe problems ofconvergence in regular single determinant calculations. These aredifficult to overcome even with codes that can impose and handlenon-Aufbau configurations, such as ADF. In turn, the physical situ-ation can be well accounted by the multi-determinant route

Fig. 5. The hydrogen bond association of the f units of compound 1. The labels incurled brackets (indexed by A and B monomers) correspond to the ligand numberingin the bonding energy discussion.

discussed in the CASSCFþ SO calculations developed in theprevious section, here confining to the simplified Lu(III) complex,on the illustrated ground that the f shell does not participate in thebonding, and the lanthanide replacement (Lu instead Er) conserveswell the active bonding factors.

The NBO analysis shows that the ligand-to-metal regulardonation takes place with components that can be assigned to 5dand 6s virtual AOs of the lanthanide. The same thing is suggested byMulliken population, which with respect to free ion shows 0.2electron excess the s shell and 1.2 in the d one, conceivably acquiredby the donation effects. In this way, the Mulliken population onlanthanide is about þ1.6. The Hirshfeld charge analysis [15], bettersuited for ionic systems than the Mulliken conventional one, yieldsþ2.41 value for lanthanide center, between �0.85 and �0.89 fornitrate fragments and practically neutral, þ0.02 aqua ligands in thecomplex.

A rather spectacular result is the supramolecular associationenergy obtained by computing the [Lu(NO3)4(H2O)2]2

2� dimer,taking the [Lu(NO3)4(H2O)2]� monomeric anions as pre-definedfragments. The total stabilization energy, �3 kcal/mol, is nicely inthe range expected for hydrogen bonding. However, the absolutevalue should be considered an approximate estimation, given thegeneral caveats pointing certain intrinsic problems of DFT methodsin the long range terms [16].

The association is gained against the net electrostatic repealbetween anions and the quantum effect of Pauli’s repulsion. Theorbital stabilization is due to relatively significant covalencecontained in the weak O/H bonding, as the prevalence of orbitalstabilization shows. The NBO donor–acceptor perturbation esti-mation between corresponding fragments {2A} with {5B} or {5A}with {2B} (see Fig. 5), due to virtual bond orbitals of aqua ligand andouter lone pairs of the nitrate, amounts in total to �11.75 kcal/mol.This value must be qualitatively considered as a part of the orbitaleffects, in alternative estimation.

4. Conclusions

The work presented interdisciplinary, experimental and theo-retical, insight into the bonding regime and magnetic properties ofa new d–f system, whose cation and anion constitutive complexunits are related in lattice by hydrogen bonds emerging fromcoordinated aqua ligands. The ab initio multi-configuration andspin orbit (CASSCFþ SO) treatment of the [Er(NO3)4(H2O)2]� unitrevealed the anisotropic magnetization tensor, in its relativeorientation to the molecular frame. The ab initio insight into themagnetic properties was found in line with the experimental data.A complementary DFT analysis devoted to the energy of complex-ation and supramolecular association, revealed data in line with thechemical intuition. The chemical inertness of the f shell and thequestion of non-Aufbau configuration of lanthanide complexes

M. Ferbinteanu et al. / Solid State Sciences 11 (2009) 760–765 765

were illustrated in the connection with the debated bondingproblems.

Acknowledgement

FC acknowledges funds from CNCSIS–UEFISCU grant ‘‘Idei’’ 174/2007. MF thanks for the support from JSPS and Tohoku University.The authors thank ‘‘Co-Laborator’’ center and Professor V. Cristea atPolytechnic University Bucharest for Matlab support.

Appendix. Supplementary materials

Supplementary data associated with this article can be found inthe online version, at doi:10.1016/j.solidstatesciences.2008.06.008.

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